Early Battery Degradation Forecasting

• Early Battery Degradation Trajectory Forecasting is a research field that infers the complete battery degradation path from limited early-cycle observations, including capacity fade and resistance rise.
• Key methodologies, such as direct regression, latent-state rollout, and milestone-centric models, achieve high accuracy with errors often below 2% in benchmark studies.
• Recent approaches integrate probabilistic models, dynamic neural architectures, and SciML techniques to enhance uncertainty quantification, interpretability, and real-world deployment.

Early Battery Degradation Trajectory Forecasting (BDTF) denotes the problem of inferring a battery’s future degradation path from an early or partial observation window, typically in terms of capacity or state of health (SoH) as a function of cycle count or time. In the recent literature, BDTF spans several closely related formulations: direct prediction of the full future capacity or SoH trajectory, joint prediction of coupled health trajectories such as capacity fade and resistance rise, latent-state rollout models that propagate degradation dynamics forward, online multistep forecasting under single-pass constraints, and milestone-centric approaches that identify or predict knee-onset, knee, and end-of-life (EoL) events as structural landmarks of the future trajectory (Li et al., 2021, Kim et al., 2023, Lim et al., 11 Mar 2026, Rico et al., 19 Sep 2025, Zhang et al., 2023). Closely adjacent work predicts only cycle life or cycle-life ranges from early degradation signals; such studies do not forecast the full trajectory directly, but they remain important because they identify early-life descriptors and uncertainty formalisms that are transferable to trajectory forecasting (Zhang et al., 2022, Singh et al., 2021).

1. Task scope and forecast targets

BDTF is broader than remaining useful life estimation. In the most direct formulation, the target is the entire future map from cycle index to capacity or SoH. One line of work predicts both capacity fade and power fade simultaneously, where power fade is represented by internal resistance rise, and derives knee-points and multiple EOL thresholds from the predicted curves; this model forecasts both trajectories “in one shot from as few as 100 cycles” (Li et al., 2021). Another line predicts a few future milestone cycles at fixed retention levels and reconstructs the full capacity trajectory by monotone interpolation, so the forecast object is still the entire degradation curve rather than only EOL (Kim et al., 2023).

Forecast targets also vary in state definition. Several papers define SoH as normalized capacity, but with dataset-specific reference choices. In the online multistep setting of iFSNet, SoH is defined from current fully charged capacity and nominal capacity, and a univariate SoH sequence of length $N=10$ is used to forecast the next $H=30$ cycles (Rico et al., 19 Sep 2025). In the world-model formulation, the model observes a window of $W=30$ cycles and jointly outputs current SoH and a future SoH trajectory over the next $H=80$ cycles (Lim et al., 11 Mar 2026). DiffBatt uses a capacity matrix constructed from the first 100 cycles to generate full future SoH curves, from which RUL is derived by threshold crossing (Eivazi et al., 2024).

A distinct but practically important subset of the literature predicts only scalar outcomes such as cycle life. Quantile Regression Forest models trained on features from the first 100 cycles produce both point predictions and 95% prediction intervals for cycle life (Zhang et al., 2022). Similarly, early-life Gaussian process regression and elastic net models predict the cycle count at which capacity falls below $80\%$ of nominal value, rather than the full future $Q(n)$ curve (Singh et al., 2021). These studies are trajectory-adjacent rather than trajectory-complete.

2. Principal modeling paradigms

Direct trajectory models in BDTF differ mainly in whether they operate in observation space, milestone space, latent space, or continuous time. A multi-task sequence-to-sequence framework based on stacked bidirectional LSTMs uses past capacity and resistance sequences as the only source of inputs, with a shared encoder and two task-specific decoders for future capacity and resistance trajectories (Li et al., 2021). A knot-based alternative predicts positive intervals $h_k$, converts them into cumulative knot cycles $p_k=\sum_{j=1}^k h_j$, and reconstructs the full retention trajectory through PCHIP; this avoids long-horizon autoregressive rollout and does not assume a parametric fade law (Kim et al., 2023).

Probabilistic nonparametric models form another major branch. Early Gaussian process work treats future capacity as a latent function of cycle number or time and studies three variants: a single-output GP, a GP with an explicit degradation-informed mean function $m(x)=a_1+a_2\exp(a_3x)$, and a multi-output GP that transfers information across cells (Richardson et al., 2017). Enhanced Gaussian Process Dynamical Models extend this idea by learning nonlinear latent dynamics and a nonlinear mapping back to observables, while allowing auxiliary observables such as midpoint temperature, midpoint voltage, and delivered energy to be incorporated without requiring their future values (Xing et al., 2022). In that formulation, EOL and RUL are downstream quantities computed from the predicted SoH trajectory.

Recent models increasingly impose explicit dynamics rather than static direct regression. The world-model formulation encodes per-cycle raw voltage, current, and temperature traces with a 1D CNN, aggregates a 30-cycle history with a PatchTST-style transformer, and propagates a latent degradation state with a residual MLP transition; current SoH and future trajectory are decoded from the latent state sequence (Lim et al., 11 Mar 2026). DiffBatt instead uses a conditional and unconditional denoising diffusion probabilistic model with classifier-free guidance and a transformer encoder for the early-life conditioning signal, generating future SoH trajectories from Gaussian noise rather than deterministic latent rollout (Eivazi et al., 2024).

Continuous-time SciML approaches replace discrete rollout with ODE integration. A Universal Differential Equation retains structured calendar and cycle degradation terms while replacing selected unknown terms with neural networks, whereas a NeuralODE models the full derivative $dq_{total}/dt$ as a neural function of time and operating variables (Murgai et al., 2024). Battery-Timer adapts a decoder-only time-series foundation model through LoRA fine-tuning and a degradation-aware trend penalty, and then distills the resulting teacher into compact expert forecasters (Chan et al., 13 May 2025). In contrast, iFSNet addresses valid online single-pass multistep forecasting by using pseudo targets from a clipped linear extrapolator, immediate per-sample updates, and an adaptive learning-rate variant iFSNet-$H=30$0 (Rico et al., 19 Sep 2025).

3. Milestone, regime, and diagnosis-informed formulations

A substantial part of BDTF is organized around degradation regime structure rather than direct curve regression. The clearest example is the curvature-based knee framework, which redefines degradation with knee occurrence as three discrete states $H=30$1 separated by two boundaries $H=30$2: beginning of life to knee-onset, knee-onset to knee, and knee to end of life (Zhang et al., 2023). The method smooths normalized capacity with a Savitzky–Golay filter, approximates discrete curvature with a successive-difference operator, and then uses STAMP, FLUSS, and REA to segment the curvature signal into stable–fluctuating–stable regimes. On the TRI LFP dataset, knee-onset versus EoL had $H=30$3, knee versus EoL had $H=30$4, and the average gap from knee-onset to knee was 323 cycles; on the SNL NMC dataset the corresponding knee-onset and knee correlations were $H=30$5 and $H=30$6, with an average knee-onset-to-knee gap of 280 cycles (Zhang et al., 2023).

A related but more deployment-oriented direction infers mechanistic state from operational snippets. The diagnostic-free onboard framework uses partial charging or discharging segments, current EFC, and a mechanistically constrained encoder-decoder to infer a latent state $H=30$7, from which full reference discharge curves, SOH, LLI, LAM$H=30$8, and LAM$H=30$9 are reconstructed; those latent variables, together with current SOH and EFC, are then used to predict future capacity degradation curves and cycle life without requiring historical raw trajectories at inference time (Che et al., 10 Mar 2025). This is not a pure sequence forecaster, but it is directly trajectory-relevant because prognosis is conditioned on an internal degradation state rather than only a scalar health summary.

The transition-model pipeline of Greenbank and collaborators is also milestone-aware in practice, even though it learns interval-wise $W=30$0 rather than explicit event labels. Automated feature extraction from voltage, current, and temperature is followed by GPR on capacity increments, and the accumulated trajectory is used to compute both knee point and EOL; the reported median root mean square errors on capacity estimates were under $W=30$1, with median knee point and EOL prediction errors of $W=30$2 and $W=30$3 (Greenbank et al., 2021). Under dynamic randomized cycling, chemistry-aware random-forest models forecast cycle life and the existence of a future knee point from the first 50 cycles, while also linking early electrical features to six XPS-derived failure-mechanism classes (Li et al., 25 Mar 2025).

4. Data regimes and representations

The literature uses markedly different input regimes. Capacity-only and SoH-only models remain common because they are simple and robust. The multi-task seq2seq model uses only past capacity and internal resistance sequences, without further feature engineering (Li et al., 2021). iFSNet uses only a univariate SoH sequence, deliberately avoiding voltage, current, or temperature covariates (Rico et al., 19 Sep 2025). Model-free knot prediction uses only early-cycle voltage, current, and time, resampled to fixed-length sequences before CNN processing (Kim et al., 2023).

Other models exploit richer per-cycle raw measurements. The world model uses discharge-time voltage, current, and temperature traces for each observed cycle, each padded or truncated to $W=30$4 time steps, and excludes discharge capacity and internal resistance from the inference input (Lim et al., 11 Mar 2026). DiffBatt conditions on a capacity matrix derived from the first 100 cycles, following the representation introduced in prior work by Attia and collaborators (Eivazi et al., 2024). Battery-Timer works with capacity degradation sequences extracted from approximately 10 GB of open-source charge-discharge records and tokenized as non-overlapping segments for a decoder-only transformer (Chan et al., 13 May 2025).

Mechanism-aware approaches often use more structured engineered features. Under randomized fast-charging protocols, the chemistry-aware framework constructs a polynomial-scale feature space of 112,900 features from $W=30$5, $W=30$6, $W=30$7, $W=30$8, $W=30$9, and $H=80$0, using seven cycle groups and four signal segments, and augments the electrical data with 552 XPS spectra from 56 post-mortem cells to identify six distinct failure mechanisms (Li et al., 25 Mar 2025). Early cycle-life range prediction from the Severson dataset uses 33 features and then selects 12, with the variance and minimum of $H=80$1 emerging as the most important (Zhang et al., 2022). In LTO-focused work, DVA, instantaneous discharge voltage, charge duration trends, and text-serialized battery records are combined in a BERT-based scalar regressor; this is not direct trajectory forecasting, but it is trajectory-relevant because the features are explicitly intended to detect early degradation signatures (Yunusoglu et al., 30 Jan 2025).

Dataset diversity is similarly uneven. Frequently reused corpora include the Severson/Toyota Research Institute LFP dataset, Sandia National Laboratories NMC and chemistry-comparison datasets, NASA PCOE cells, MIT, CALCE, RWTH, HUST, HNEI, UL_PUR, and proprietary or newly generated dynamic-cycling datasets (Zhang et al., 2023, Eivazi et al., 2024). Several papers remain confined to one chemistry and one controlled protocol family, whereas others deliberately test cross-chemistry or cross-condition generalization.

5. Evaluation practices and empirical results

Direct full-trajectory models now report competitive quantitative accuracy. The knot-based reconstruction method achieved mean absolute percentage errors in trajectory prediction below $H=80$2 for all cases of two to four knots on 169 Severson cells, and with three-cycle input the trajectory prediction error was $H=80$3 Ah and $H=80$4 MAPE (Kim et al., 2023). The multi-task sequence-to-sequence model reported an average percentage error of $H=80$5 for capacity fade and $H=80$6 for resistance rise, with median absolute errors of 38 cycles for EOL80, 33 cycles for EOL65, 55 cycles for the capacity knee-point, 41 cycles for EOL120, 34 cycles for EOL130, and 61 cycles for the resistance knee-point (Li et al., 2021).

Models with explicit dynamics show the importance of rollout. In the world-model study, iterative latent rollout roughly halved short-horizon trajectory MAE relative to direct regression from the same encoder: at horizon 5, WM achieved $H=80$7, PIWM $H=80$8, and CNN-PatchTST $H=80$9; at horizon 50, WM remained lower at $80\%$0 versus $80\%$1 for direct regression (Lim et al., 11 Mar 2026). In online single-pass multistep forecasting, iFSNet-$80\%$2 achieved $80\%$3 RMSE and $80\%$4 MAE on smooth degradation trajectories and $80\%$5 RMSE and $80\%$6 MAE on irregular trajectories with capacity regeneration spikes (Rico et al., 19 Sep 2025).

Probabilistic generative models provide a complementary evaluation picture. DiffBatt, conditioned on the first 100 cycles, reported a mean RUL RMSE of 196 cycles across all datasets and mean SOH-trajectory RMSE values of $80\%$7 at 90% EOL and $80\%$8 at 80% EOL (Eivazi et al., 2024). In the transition-model work based on automated feature extraction and GPR on $80\%$9, the approach produced median root mean square errors on capacity estimates under $Q(n)$0, and median knee point and EOL prediction errors of $Q(n)$1 and $Q(n)$2 (Greenbank et al., 2021).

Milestone-oriented methods are often evaluated differently. The curvature-based knee framework uses correlation between identified event locations and EOL rather than direct landmark timing error; on the TRI dataset, proposed knee identification performance was $Q(n)$3 and knee-onset identification performance was $Q(n)$4, while on the SNL dataset the same quantities were $Q(n)$5 and $Q(n)$6, substantially above the double Bacon–Watts benchmark (Zhang et al., 2023). Under dynamic randomized cycling, chemistry-aware early prognostics on the first 50 cycles achieved a test MAPE of $Q(n)$7 and a test RMSE of 136.96 for life prediction, and the same feature space supported accurate knee-point existence prediction and XPS-pattern classification (Li et al., 25 Mar 2025).

6. Uncertainty, interpretability, and deployment

Uncertainty treatment is highly uneven across BDTF. Gaussian process models offer predictive means and variances natively, and early GP work used trajectory credibility intervals and threshold crossing of upper and lower confidence bounds to derive EOL uncertainty (Richardson et al., 2017). Quantile Regression Forest models use conditional quantiles rather than Gaussian assumptions; with the proposed alpha-logistic-weighted criterion, a 95% cycle-life interval predictor achieved PICP $Q(n)$8, MPIW $Q(n)$9 cycles, and AIS $h_k$0 cycles on the Severson dataset (Zhang et al., 2022). DiffBatt quantifies uncertainty through multiple generated SOH trajectories and reports the standard deviation of RUL across ten samples (Eivazi et al., 2024). By contrast, several otherwise trajectory-relevant papers do not provide calibrated probabilistic outputs.

Interpretability likewise ranges from feature importance to mechanistic latent states. In QRF-based early life prediction, permutation importance and partial dependence plots identify the variance and minimum of $h_k$1 as the two dominant predictors, and interval width correlates strongly with absolute prediction error (Zhang et al., 2022). The diagnostic-free onboard framework constrains its latent space to $h_k$2, permitting direct interpretation in terms of LLI, LAM$h_k$3, and LAM$h_k$4 (Che et al., 10 Mar 2025). The chemistry-aware dynamic-cycling study ties early electrical features to six XPS-derived degradation regimes, including lithium-plating-dominated and inorganic-SEI-rich patterns (Li et al., 25 Mar 2025). In the world-model study, the SPM-inspired physics term did not improve aggregate MAE relative to the unconstrained world model, but it reduced knee-region MAE from $h_k$5 to $h_k$6 in Stage 2 while worsening Stage 3 MAE from $h_k$7 to $h_k$8 (Lim et al., 11 Mar 2026).

Deployment constraints increasingly shape model design. iFSNet was reported at about $h_k$9 s per iteration, supporting online adaptation in single-pass mode (Rico et al., 19 Sep 2025). Battery-Timer fine-tunes an 84M-parameter Timer backbone with LoRA, where learnable LoRA parameters are only $p_k=\sum_{j=1}^k h_j$0 of the total, and then distills the teacher into compact expert models for edge deployment (Chan et al., 13 May 2025). The diagnostic-free onboard framework is explicitly designed to avoid diagnostic cycles and long historical memory, relying instead on a single partial operational snippet plus current EFC (Che et al., 10 Mar 2025).

7. Limitations and research directions

The literature does not converge on a single early-forecasting protocol. Some papers evaluate strict early-prefix prediction from the first one, three, or one hundred cycles (Kim et al., 2023, Eivazi et al., 2024), while others use rolling windows at arbitrary life stages (Lim et al., 11 Mar 2026) or endpoint-only prediction from the first 100 cycles (Zhang et al., 2022). Several scientifically important studies are only partially aligned with strict early BDTF: the SciML UDE/NeuralODE work learns long-horizon degradation dynamics but does not clearly define an early-prefix protocol (Murgai et al., 2024); Battery-Timer demonstrates long-context trajectory forecasting and cross-condition transfer, but its main validation uses input length 480 and output length 196 rather than a very-early-life setup (Chan et al., 13 May 2025).

A second limitation is that some approaches predict only milestones or endpoints, not the full future path. Knee-onset identification, cycle-life range prediction, early cycle-life regression, and knee-point existence classification are all valuable, but they do not directly output $p_k=\sum_{j=1}^k h_j$1 or SoH$p_k=\sum_{j=1}^k h_j$2 over the remaining life (Zhang et al., 2023, Zhang et al., 2022, Singh et al., 2021, Li et al., 25 Mar 2025). Conversely, some full-trajectory models require assumptions that weaken deployment realism, such as perfect knowledge of future cell use in transition-based GPR forecasting (Greenbank et al., 2021), a fixed nonincreasing pseudo-target slope in online learning (Rico et al., 19 Sep 2025), or training-time access to auxiliary measurements such as internal resistance (Lim et al., 11 Mar 2026).

A third limitation is restricted validation scope. Many studies remain cell-level, laboratory-scale, and chemistry-specific. Cross-chemistry generalization is tested in some settings, but pack-level coupling, future usage uncertainty, field telemetry irregularity, and uncertainty calibration remain underdeveloped. This suggests that the next phase of BDTF will likely combine several strands already visible in the literature: regime landmarks such as knee-onset and knee, mechanistically interpretable latent states, probabilistic trajectory generators, and scenario-conditioned forecasting under changing future duty cycles. A plausible implication is that the strongest future systems will not choose between direct trajectories and events, but will jointly forecast the curve, its regime boundaries, and the uncertainty around both.